Digit Sums:
$S_b(n)$ is the sum of digits of $n$ in base $b$
$S_2(1396^{96}) = 396$
$S_{129}(1396^{1396}) = 96 \times 1396$
$S_{699}(1396^{1396}) = 379 \times 1396$
$S_{1048}(1396^{1396}) = 547 \times 1396$
$S_{1397}(1396^{1396}) = 691 \times 1396$
$S_{1725}(1396^{1396}) = 846 \times 1396$
Permutations:
$1396 =$ the number of permutations $\pi\in S_7$ such that $2\pi(1)-1,\ldots,2\pi(7)-7$ are distinct.